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Resistance equivalent to a circuit

  1. Sep 29, 2009 #1
    Hi,

    Suppose I have the following circuit (excuse the ugly drawing):
    fm6m14.png

    Suppose the generator is 1A and all the resistance are 1 Ohm (the values are not important). Moreover, suppose I already have all the voltages in V1, V2, V3, V4 (which I got using nodal analysis), and V0 is set to ground (V0 = 0).

    How do I get the total resistance from point A to point B (or node V0)? Can I use the results I got from nodal analysis for this?


    Please note my knowledge of electrical circuits is very basic, as this is not my field. I am using this to build an artificial Hex player, and resistance provides a good connectivity measure from each side of the board (see page 2 in http://home.earthlink.net/~vanshel/VAnshelevich-01.pdf).
     
  2. jcsd
  3. Sep 29, 2009 #2
    The voltages of V1 and V2 must be the same since they are connected by a wire.

    The voltages of V3 and V4 must be zero since they are connected together by a wire which is also connected to ground.

    For this circuit, since you are exciting it with a current source of 1 amp, then the resistance from A to B (ground) is equal to the voltages at V1 and V2, which are the same.
     
  4. Sep 30, 2009 #3

    vk6kro

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    Science Advisor

    Any resistors you have shorted out can be replaced by wires.

    That only leaves 3 resistors in parallel in the middle of the diagram.

    They are all 1 ohm, so ....... what is the total resistance?
     
  5. Sep 30, 2009 #4
    Are you saying that the resistance from A to B is R = V1/I = V1 Ohm = V2 Ohm?

    Also, why is the voltage the same in V1 and V2, if current can flow from A to V1 and V2? Shouldn't V1 and V2 have a lower potential than A?

    @vk6kro: I wanted to avoid that kind of analysis, since this circuit is not "fixed". Its just the simplest case of a much larger circuit that may look different (resistances with value=+infinite or 0), and I want a way to solve this that is easy to code into a program that does it (an algorithm, so to speak).

    Thanks!
     
  6. Sep 30, 2009 #5
    Exactly.

    The voltage is the same at V1 and V2 because they are connected together by a wire.

    In schematics such as you have shown, a simple line represents a wire, which is assumed to have zero resistance.

    Real wires don't have zero resistance. They have some finite, non-zero resistance, but if you want to treat that in a circuit you would usually insert a resistor symbol of some low value like 500 microhms to represent the wire resistance. In the absence of any such representation of the non-zero resistance of a wire, the wire is treated as though it has zero resistance.
     
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